Case Study Practice for Eduqas GCSE Statistics | Eduqas GCSE 统计案例分析实战演练

📚 Case Study Practice for Eduqas GCSE Statistics | Eduqas GCSE 统计案例分析实战演练

This article guides you through a complete statistical investigation using a realistic school-based scenario. By working through the steps – from planning and data collection to hypothesis testing – you will revise the core topics of the Eduqas GCSE Statistics specification and see how the techniques connect in context. Each section presents key ideas first in English and then in Chinese, helping you master both the subject knowledge and the bilingual terminology.

本文通过一个真实的校园场景，带领你完整地走一遍统计探究的流程。从规划、数据收集到假设检验，你将按步骤复习 Eduqas GCSE 统计课程的核心内容，并看到各种方法如何在情境中相互关联。每一节先用英文阐述重点，再用中文进行对应讲解，帮助你同时掌握学科知识和双语术语。

1. Designing the Study and Sampling Methods | 研究设计与抽样方法

A school wishes to investigate the relationship between the number of hours students spend on independent study per week and their end-of-year exam scores. The first step is to define the population – all Year 11 students in the school – and decide how to select a representative sample. A simple random sample of 50 students could be obtained by assigning each student a number and using a random number generator. However, to ensure fair representation of genders or classes, a stratified sample might be more appropriate: the population is divided into strata (e.g., male/female), and a random sample is taken from each stratum in proportion to its size.

一所学校希望调查学生每周自主学习的小时数与年终考试成绩之间的关系。第一步是确定总体——学校所有 Year 11 学生——并决定如何选取一个具有代表性的样本。可以将每个学生编号，使用随机数生成器抽取 50 名学生作为简单随机样本。然而，为了确保性别或班级的代表性，分层抽样可能更加合适：将总体划分为层（例如男生/女生），然后按各层所占的比例从每层中随机抽取样本。

Before any data collection, ethical considerations must be addressed. Students should be informed about the purpose of the study, give their consent, and be assured that their responses will remain confidential. The sampling method should also be practical: there may be absentees on the day, which could bias the results if not accounted for.

在任何数据收集之前，必须考虑伦理问题。学生应被告知研究目的，获得他们的同意，并确保回答会被保密。抽样方法也应当切实可行：如果在调查当天有学生缺席且不加以处理，可能会导致结果出现偏差。

2. Data Collection: Questionnaires and Variables | 数据收集：问卷与变量

A well-designed questionnaire is prepared to collect data on: (i) average hours of independent study per week (a numerical continuous variable); (ii) gender (categorical); (iii) whether the student has a part-time job (categorical binary: Yes/No); and (iv) end-of-year exam percentage score (numerical continuous). The questionnaire should be pre‑tested on a small group to identify any ambiguous or leading questions. In this investigation, the intended response variable is exam score, and the main explanatory variable is study hours; gender and job status may act as additional explanatory variables.

一份精心设计的问卷被用来收集以下数据：(i) 每周自主学习的平均小时数（连续数值型变量）；(ii) 性别（类别型）；(iii) 学生是否有兼职工作（二分类别型：是/否）；(iv) 年终考试百分比成绩（连续数值型）。问卷应在一个小群体中预先测试，以发现模糊或诱导性的问题。在本项调查中，目标响应变量是考试成绩，主要的解释变量是学习时间；性别和工作状态可作为附加的解释变量。

3. Organising and Representing Data: Frequency Tables and Charts | 数据整理与表示：频率表与图表

Once the sample data are collected, the study hours can be summarised into a grouped frequency table using intervals such as 0–5, 5–10, …, 20–25 hours. From this table a histogram is drawn, ensuring the vertical axis shows frequency density (frequency ÷ class width) so that the area of each bar is proportional to frequency. For the categorical variable ‘part-time job’, we can use a bar chart or a pie chart to display the proportions of ‘Yes’ and ‘No’ answers clearly.

收集到样本数据后，可以将学习时间汇总到组距频率表中，区间例如 0–5 小时、5–10 小时……20–25 小时。根据该表绘制直方图，确保纵轴显示频率密度（频率 ÷ 组距），使每个条形的面积与频率成正比。对于分类变量“兼职工作”，可以使用条形图或饼图来清晰展示“有”和“无”两种答案所占的比例。

For exam scores, a cumulative frequency graph can be constructed by adding a cumulative frequency column to the grouped table and plotting the upper class boundaries against cumulative frequency. This graph allows us to estimate the median, quartiles and inter‑percentile ranges smoothly.

对于考试成绩，可以在分组表中添加一列累积频率，并以组上限为横坐标、累积频率为纵坐标，绘制累积频率图。通过该图我们可以较为精确地估计中位数、四分位数以及百分位距。

4. Measures of Central Tendency and Spread | 集中趋势与离散度量

For the exam scores (expressed as percentages), the mean x̄ provides an average, the median identifies the central position, and the mode indicates the most frequent score. Suppose from the sample of 50 students we calculate a mean of 68% and a median of 70%. The difference suggests a slight negative skew. Measures of spread describe how varied the scores are: the range (maximum minus minimum) gives a very basic picture, but the interquartile range IQR = Q₃ − Q₁ is more robust against outliers.

对于考试成绩（以百分比表示），均值 x̄ 给出平均水平，中位数指明中心位置，众数指出最常出现的分数。假设从 50 名学生样本中计算出均值为 68%，中位数为 70%，这个差异提示分布可能略呈负偏态。离散度量描述分数的变异程度：极差（最大值减最小值）提供了最为粗略的图像，而四分位数间距 IQR = Q₃ − Q₁ 对异常值更加稳健。

The standard deviation σ (or s for a sample) quantifies the typical distance of data points from the mean

Published by TutorHao | Year 11 统计 Revision Series | aleveler.com

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